The distribution of the discrete tree length on a line
The distribution of the interval between events of a Cox process with shot noise intensity.
The efficiency of variance reduction in manufacturing and service systems: the comparison of the control variates and stratified sampling.
The empirical TES methodology: Modeling empirical time series.
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
The escape model on a homogeneous tree.
The expected cumulative operational time for finite semi-Markov systems and estimation
In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
The expected discounted reward from a Markov replacement process
The extreme gap in the multivariate Poisson process
The failure rate in reliability: Approximations and bounds.
The failure rate in reliability. Numerical treatment.
The fermion number processes as a functional central limit of quantum hamiltonian models
The first exit of almost strongly recurrent semi-Markov processes
Let , n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged...
The foundations of probability with black swans.
The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...
The GI/G/1 model with warming-up time
The incipient infinite cluster in high-dimensional percolation.
The infinite valley for a recurrent random walk in random environment
We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the – suitably centered – empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov, see Comm. Math. Phys.92 (1984) 491–506. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the...
The Intermittent Server
The jammed phase of the Biham-Middleton-Levine traffic model.